Zumdahl’s Chapter 11

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Zumdahl’s Chapter 11. Solutions. Solution Composition Concentrations H solution Hess’s Law undersea Solubilities Henry’s Law: Gases and Raoult’s Law Temperature Effects. Colligative Properties T BP Elevation T FP Depression Osmotic Pressure van’t Hoff Factor

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## Zumdahl’s Chapter 11

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### Zumdahl’s Chapter 11

Solutions

Solution Composition

Concentrations

Hsolution

Hess’s Law undersea

Solubilities

Henry’s Law: Gases

and Raoult’s Law

Temperature Effects

Colligative Properties

TBP Elevation

TFP Depression

Osmotic Pressure

van’t Hoff Factor

Colloids and Emulsions

Chapter Contents
Solution Composition
• Molarity, M = moles solute / liter sol’n.
• Cannot be accurately predicted for mixtures because partial molar volumes vary.
• If volumes don’t add, masses and moles do!
• Molality, m = moles solute / kg solvent
• Not useful in titration unless density known.
• Useful in colligative effects.
• Mole fraction, XA = moles A / total moles
Conc. of 50% by wt. NaOH
• Density at 20°C is 1.5253 g cm3
•  each liter of solution weighs 1525.3 g
• ½ that mass is NaOH, or 762.65 g
• nNaOH = 762.65 g [ 1 mol/39.998 g ] = 19.067
• [NaOH] = 19.067M but also
• 19.067 mol / 0.76265 kg H2O = 25.001mand
• nwater = 762.65 g [ 1 mol/18.016 g ] = 42.332
• XNaOH =19.067 /(19.067+42.332)=0.31054
100 cc ea. H2O & C2H5OH
• Want Proof? 50% by Volume 100 proof
• Want Volume? Need densities!
• At 20°C,  = 0.99823 & 0.79074 g/cc, resp.
•  sol’n. mass = 99.823+79.074 = 178.897 g
• By mass: 100%(79.074 / 178.897) = 44.201%
• From tables:  = 0.92650 g/cc
• V = 178.897 g/0.92650 g/cc = 193.09 cc
•  It’s really 2 100cc / 193.09 cc = 103.58 proof

Expand both solvent and solute

• at the expense of H1 and H2
• in lost intermolecular
• interactions.
Conceptual Mixing Enthalpies
• Merge the
• expanded liquids
• together recovering
• H3 from the
• new interactions.

But even if it

requires heat,

mixing may

well happen

since entropy

favors it!

3. If the exothermic

mixing exceeds

the endothermic

expansion, there

will be a net exo-

thermic heat of

solution.

Underwater Hess’s Law
• Since solutions are fluid, they need not expand then mix, requiring “upfront” \$\$.
• Instead they acquire AB interaction as they lose AA and BB ones; pay as you go.
• Hess doesn’t care; the overall enthalpy change\$ will be the same.
Solubilities
• It’s true that which of A or B is the solute or solvent is mere naming convention …
• Which was the solute in that 50% cocktail?
• Still solutes with low solubility are surely in the mole fraction minority.
• And it is worthwhile asking what state parameters influence their solubility?
Gas Solubilities
• No doubt about it: pressure influences solubility. And directly.
• CO2 in soft drinks splatter you with dissolution as you release the pressure above the liquid.
• Henry’s Law codifies the relationship:
• PA = kH•[A(aq)] (kH is Henry’s constant)
• It applies only at low concentrations; so
• It applies not at all to strongly soluble gases!
Apply at opposite extremes.

Raoult when X~1

Henry when X~0

So Raoult to solvent and Henry to solute.

When XB is small, XB=[B]/55.51M for [water]=55.51M

Henry’s OK with X.

P°B

P°A

P

k’H;B

k’H;A

XA

0

1

P = P° X

P kH’ X

Raoult’s and Henry’s Laws
Raoult vs. Henry Difference
• When X~1, the solvent is not perturbed by miniscule quantities of solute. Solvent vaporization is proportional to solvent molecules at solution’s surface. Raoult
• When X~0, solute is in an utterly foreign environment, surrounded only by solvent. kH reflects the absence of A-A interaction, and Henry applies.
Solubility and Temperature
• Sometimes the AB interactions are so much weaker than AA or BB that A and B won’t mix even though entropy favors it.
• Since T emphasizes entropy, some of the immiscible solutions mix at higher T.
• Solidsolubilities normally rise with T.
• Exceptions are known … like alkali sulfates.
Gases Flee Hot Solutions
• You boiled lab water to drive out its dissolved gases, especially CO2.
• That’s why boiled water tastes “flat.”
• Genghis Khan invented tea (cha) to flavor the water his warriors refused to boil for their health as they conquered Asia and Eastern Europe.
• Increased T expands Vgas, making it more favored by entropy vs. dissolved gas.
• This time, no exceptions!
The Phase Diagram

Mixing in a solute lowers solvent Pvapor

So TBP must rise.

Since the solvent’s solid suffers no Pvapor change, TFP must fall.

Liquid span must increase in solution.

P

T

Changed Phase Changes
Elevating Depressions
• Both colligative properties arise from the same source: Raoult’s Law.
• Thermo. derivations of resulting T give:
• Freezing Point Depression:
• TFP = –Kf msolute where Kf~RTFP2 / Hfusion
• Boiling Point Elevation:
• TBP = +Kb msolute where Kb~RTBP2 / Hvap
• Kf > Kb since Hfusion < Hvap
Antifreeze / Summer Coolant are the same

Ethylene glycol (1,2-Ethanediol) is soluble in the radiator water, non-corrosive, nonscaling, and raises the boiling point in summer heat while lower-ing freezing point in winter.

“Road salt” is CaCl2 now since NaCl corrodes cars.

Practical Phase Changes
Colligative Utility
• Ligare means “to bind.” These features are bound up with just numbers of moles.
• NOT the identity of the molecules!
• Indeed, Kf and Kb are seen not to depend on solute properties but on solvent ones.
• So they’re used to count solute moles to convert weights to molar weights!
• Not sensitive enough for proteins, MW~10 kg
Exquisite Sensitivity
• To count protein moles, we need Osmotic Pressure that is very sensitive to [solute].
• Solvent will diffuse across a membrane to dilute a concentrated solute solution.
• If the solute is too large (protein!) to diffuse back, the volumemust increase.
• Rising solution creates (osmotic) pressure to an equilibrium against further diffusion.

MW by Osmotic Pressure, 
• Thermodynamic derivation of the balance between  & diffusion on the equilibrium gives: V = nRT(!) or = MRT
• E.g., 0.5 g in 50 cc yields 10 cm of pressure at 25°C (so RT = 24.5 atm L /mol)
• 10 cm (1 ft/30.5 cm) (1 atm/33 ft) = .010 atm
• [protein] =  / RT = 0.00041 mol/L
• Wt = 0.5 g/0.05 L = 10 g/L MW = 24 kg
Moles of What?
• Doesn’t matter if property’s colligative.
• Counts moles of ions if solute dissociates.
• van’t Hoff Factor, i, measures ionization.
• i multiplies molality in any of the colligative expressions to show apparent moles present.
• It’s a stand-in for non-idealities too; pity.
• So in 0.001mK3PO4, i should be nearly 4, and colligative properties see 0.004m?NO!
Weak Electrolyte Corrections
• PO43– is a conjugate base of HPO42–
• Ka3 = 4.810–13so Kb1 = Kw/Ka3 = 0.021 for PO43– + H2O  HPO42– + OH–
• Equilibrium lies to left, so start with [OH–] = [HPO42–] = 0.001–xand [PO43–] = x
• (0.001–x)2 / x = 0.021 or x ~ 4.810–5 ~ 0
• Counting K+, total moles ~ 0.003+2(0.001)
• Soi ~ 0.005/0.001 = 5not 4. (4.95 with care)
Reverse Osmosis
• If dilution across a semipermeable (keeps out solute) membrane builds pressure,
• Pressure should be able to squeeze water back out of a solution! …if the membrane survives.
• Desalination plants are critical in desert nations like the Gulf States & N. Africa.
• Waste water is much more (salt) concentrated, an environmental hazard to local sea life unless ocean currents are swift enough to dilute it.
When is a SolutionNot a Solution?
• When it’s a problem? 
• Insoluble materials precipitate out of a solution at a rate that increases with their mass. So smallparticlesstay suspended.
• With particle sizes of 1 m to 1 nm such suspensions are called colloids.
• Since visible ~ 0.5m, the larger colloids scatter visible light efficiently! (Tyndall effect)
Taxonomy of Suspensions

Dispersed Material Phase

Dispersing Medium Phase

+

+

+

+

+

+

+

+

+

Aqueous Colloids
• Particles might be charged and stabilized (kept from coagulating) by electrostatics.
• Even neutral ones will favor adjacency of one charge which develops double layer (an oppositely charged ionic shell) to stabilize the colloid.
• “Salting out” destroys the colloid by over-whelming the repulsions with ionic strength.
• Small, highly charged ions work best, of course.
Surface Chemistry (liquids)
• Colloid study, a subset of surface science.
• Colloid molecules must be insoluble in the dispersing medium.
• Solubility governed by “like dissolves like.”
• But surface tensions play a role as well since solutes display surface excess concentration.
• Interfaces between phases are not simply at the bulk concentrations; influences segregation.
Surface Chemistry (solids)
• Industrial catalysts for many processes are solids.
• Atoms and molecules adhere, dissociate, migrate, reassociate, and desorb.
• Efficiency scales with catalyst surface area.
• Area measured by adsorbing monolayers of gas (N2 ) and observing discontinuities as monolayer is covered.